"Just what do we mean by a 'proof'? It seems that mathematicians - and to avoid generating too many letters of complaint, let me hasten to rephrase that as 'we mathematicians' - are somewhat schizophrenic when it comes to answering this question. When pressured by the persistent student, we fall back on the logician's definition and the 'translatable in principle' defense. But in practice, we work happily with what is quite clearly a socially determined notion of proof."